It depends on your girth, or butt size if that helps. Most older male adults would be happy with about 28", give or take a coupla inches. Even so, you'll often back into the other side. I would advise using screws here and there into studs to keep the whole from budging. When you back into the other side, the whole thing will shake and knock over rolling stock if you don't firm it up into the studs. Use cleats if you must.
That lower left shaded curve is very tight. If you were to angle the turnout above it on the diagram to our left about 6 deg. and then make a wider curve to the lower turnout, you would probably increase your radius by at least two inches, which might matter in the future.
Your staging, if you really want/need it, would be at top center where that track appears to terminate. At the last turnout, you commence a descent of about 3-3.5%. By the time the train gets to the apparent stub end, it will have descended approximately three inches, maybe more (I haven 't calculated it, but I'm close...). It would continue its descent through a tunnel portal for another six-8 feet and then level into a yard with a throat and several ladders, each with a well-built backstop at the ends. You would also wire the staging separately using a two way switch to keep locomotives from sitting there using power but doing nothing. You want staging to be silent and unpowered until you want to place a consist or bring one up to level ground.
If the math doesn't work as I've described, commence the descent halfway along the left side with another turnout. That would buy you about 6-8" by the time it disappears at the top center. All of this means you'll have at least bi-level trackage on the surface, but it's doable, and should be fun. More terrain and chances for imagination and scenery interest.
You can get away with less height difference, too. It would be tight, but 9" would suffice. You only need to be able to reach in safely and retrieve or to rerail something, or to flick a set of points.
